On spectral energy transfer in convective turbulence
DOI:
https://doi.org/10.7242/1999-6691/2016.9.2.11Keywords:
convective turbulence, energy cascade, shell modelsAbstract
The specific features of cascade processes in fully developed turbulence that exists against the background of a density (temperature) gradient are investigated. The gradient is either parallel (turbulence in a stably stratified medium) or anti-parallel (convective turbulence) to the gravitational force. We mainly address the question of realizability of the Obukhov-Boldgiano regime (OB), which implies a balance between buoyancy forces and nonlinear interactions in an extended part of the inertial range. There are no foolproof evidences that prove the existence of OB, although the fragments of spectra with slopes, similar to “-11/5” and “-7/5”, have been observed in some numerical simulations of convective turbulence. This paper presents a critical comparison of these results with the results obtained using a shell model, which allows us to perform simulations in a wide range of governing parameters. The shell model is introduced by generalizing a class of helical shell models to the case of buoyancy driven turbulence. It is shown that, in fully developed turbulence that is characterized by a range of scales with a constant spectral energy flux, the buoyancy forces cannot compete with nonlinear interactions and, therefore, have no impact on the inertial range dynamics. In convective turbulence, exactly these forces provide turbulence with energy, but only at the largest scales. Under conditions of stable stratification, the buoyancy forces reduce the energy of turbulent pulsations. In both cases the OB regime does not appear in the inertial range, where the Kolmogorov’s “-5/3” law is established, and the temperature behaves like a passive scalar. Our simulations indicate that the previous interpretations of the observed deviations from the “-5/3” spectrum as the OB regime are wrong because they appear in the case of an insufficient separation between the buoyancy and dissipation scales.
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References
Obuhov A.M. O vlianii arhimedovyh sil na strukturu temperaturnogo pola v turbulentnom potoke // DAN SSSR. - 1959. - T. 125, No 6. - S. 1246-1248.
2. Bolgiano R., Jr. Turbulent spectra in a stably stratified atmosphere // J. Geophys. Res. - 1959. - Vol. 64, no. 12. - P. 2226-2229. DOI
3. Kolmogorov A.N. Lokal’naa struktura turbulentnosti v neszimaemoj vazkoj zidkosti pri ocen’ bol’sih cislah Rejnol’dsa // Doklady AN SSSR. - 1941. - T. 30, No 4. - S. 9-13.
4. Wu X.-Z., Kadanoff L., Libchaber A., Sano M. Frequency power spectrum of temperature fluctuation in free convection // Phys. Rev. Lett. - 1990. - Vol. 64. - P. 2140-2143. DOI
5. Chilla F., Ciliberto S., Innocenti C., Pampaloni E. Boundary layer and scaling properties in turbulent thermal convection // Nuovo Cimento D. - 1993. - Vol. 15, no. 9. - P. 1229-1249. DOI
6. Calzavarini E., Toschi F., Tripiccione R. Evidences of Bolgiano-Obhukhov scaling in three-dimensional Rayleigh-Benard convection // Phys. Rev. E. - 2002. - Vol. 66. - 016304. DOI
7. Kumar A., Chatterjee A.G., Verma M.K. Energy spectrum of buoyancy-driven turbulence // Phys. Rev. E. - 2014. - Vol. 90. - 023016. DOI
8. Lohse D., Xia K-Q. Small-scale properties of turbulent Rayleigh-Benard convection // Annual Rev. Fluid Mech. - 2010. - Vol. 42. - P. 335-364. DOI
9. Lozkin S.A., Frik P.G. Inercionnyj interval Obuhova-Boldziano v kaskadnyh modelah konvektivnoj turbulentnosti // MZG. - 1998. - No 6. - C. 37-46. DOI
10. Boffetta G., de Lillo F., Mazzino A., Musacchio S. Bolgiano scale in confined Rayleigh-Taylor turbulence // J. Fluid Mech. - 2012. - Vol. 690. - P. 426-440. DOI
11. Kumar A., Verma M.K. Shell model for buoyancy-driven turbulence // Phys. Rev. E. - 2015. - Vol. 91. - 043014. DOI
12. Frik P.G. Modelirovanie kaskadnyh processov v dvumernoj turbulentnoj konvekcii // PMTF. - 1986. - No 2. - S. 71-79. DOI
13. Zimin V.D., Frik P.G. Turbulentnaa konvekcia. - M.: Nauka, 1988. - 178 s.
14. Brandenburg A. Energy spectra in a model for convective turbulence // Phys. Rev. Lett. - 1992. - Vol. 69, no. 4. - P. 605-608. DOI
15. Frik P.G., Resetnak M.U., Sokolov D.D. Kaskadnaa model’ turbulentnosti dla zidkogo adra Zemli // Doklady RAN. - 2002. - T. 387, No 2. - C. 253-257.
16. Ching E.S.C., Ko T.C. Ultimate-state scaling in a shell model for homogeneous turbulent convection // Phys. Rev. E. - 2008. - Vol. 78. - 036309. DOI
17. Frik P.G. Ierarhiceskaa model’ dvumernoj turbulentnosti // Magnitnaa gidrodinamika. - 1983. - No 1. - C. 60-66.
18. Desnanskij V.N., Novikov E.A. Modelirovanie kaskadnyh processov v turbulentnyh teceniah // PMM. - 1974. - T. 38, No 3. - S. 507-513.
19. Biferale L., Lambert A., Lima R., Paladin G. Transition to chaos in a shell model of turbulence // Physica D. - 1995. - Vol. 80, no. 1-2. - P. 105-119. DOI
20. Frick P., Dubrulle B., Babiano A. Scaling properties of a class of shell models // Phys. Rev. E. - 1995. - Vol. 51. - P. 5582-5593. DOI
21. L’vov V., Podivilov E., Pomyalov A., Procaccia I., Vandembroucq D. Improved shell model of turbulence // Phys. Rev. E. - 1998. - Vol. 58. - P. 1811-1822. DOI
22. Stepanov R.A., Frik P.G., Sestakov A.V. O spektral’nyh svojstvah spiral’noj turbulentnosti // MZG. - 2009. - T. 44, No 5. - C. 33-44. DOI
23. Plunian F., Stepanov R., Frick P. Shell models of magnetohydrodynamic turbulence // Phys. Rep. - 2013. - Vol. 523, no. 1. - P. 1-60. DOI
24. Sestakov A.V., Stepanov R.A., Frik P.G. Vlianie vrasenia na kaskadnye processy v spiral’noj turbulentnosti // Vycisl. meh. splos. sred. - 2012. - T. 5, No 2. - C. 193-198. DOI
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